{"id":"https://openalex.org/W2158982567","doi":"https://doi.org/10.1017/s096354830000016x","title":"On a Correlation Inequality of Farr","display_name":"On a Correlation Inequality of Farr","publication_year":1992,"publication_date":"1992-06-01","ids":{"openalex":"https://openalex.org/W2158982567","doi":"https://doi.org/10.1017/s096354830000016x","mag":"2158982567"},"language":"en","primary_location":{"id":"doi:10.1017/s096354830000016x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830000016x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111437501","display_name":"Colin McDiarmid","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Colin McDiarmid","raw_affiliation_strings":["Department of Statistics, Oxford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Oxford University","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111437501"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.33117484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"1","issue":"2","first_page":"157","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.906499981880188,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.902899980545044,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7151917219161987},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7134362459182739},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6438969373703003},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.543788492679596},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.522038459777832},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5012562274932861},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4822414815425873},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4766022562980652},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39550235867500305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.153670072555542}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7151917219161987},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7134362459182739},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6438969373703003},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.543788492679596},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.522038459777832},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5012562274932861},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4822414815425873},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4766022562980652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39550235867500305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.153670072555542},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s096354830000016x","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s096354830000016x","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.96.3768","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.96.3768","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.stats.ox.ac.uk/~cstone/Prof. C. McDiarmid Publications/1992/farr3.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W77813785","https://openalex.org/W97263645","https://openalex.org/W169898132","https://openalex.org/W1998090738","https://openalex.org/W2017722258","https://openalex.org/W2082338474","https://openalex.org/W2097612342","https://openalex.org/W2319158417","https://openalex.org/W2482182218","https://openalex.org/W2573642654"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W1585007175","https://openalex.org/W2369178846","https://openalex.org/W2082716031","https://openalex.org/W2382521049","https://openalex.org/W2370289839","https://openalex.org/W2144385241","https://openalex.org/W2933494595","https://openalex.org/W4313347705"],"abstract_inverted_index":{"Suppose":[0],"that":[1,34,37,45,59],"each":[2,38],"vertex":[3],"of":[4,27,55,73,76],"a":[5,9,70],"graph":[6],"independently":[7],"chooses":[8],"colour":[10],"uniformly":[11],"from":[12],"the":[13,24,35,46,53,56,60],"set":[14,26,39],"{1,":[15],"\u2026,":[16],"k":[17,57],"};":[18],"and":[19],"let":[20],"S":[21,40,62],"i":[22,30,41,63],"be":[23],"random":[25],"vertices":[28],"coloured":[29],".":[31],"Farr":[32],"shows":[33],"probability":[36],"is":[42,48,50],"stable":[43],"(so":[44],"colouring":[47],"proper)":[49],"at":[51],"most":[52],"product":[54],"probabilities":[58],"sets":[61],"separately":[64],"are":[65],"stable.":[66],"We":[67],"give":[68],"here":[69],"simple":[71],"proof":[72],"an":[74],"extension":[75],"this":[77],"result.":[78]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}